Re: D01-24
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15 Jun 2020, 04:13
The wording in this question is somewhat misleading. I am interpreting the language "The following day the buses do the return trip at the same constant speed." to imply that the buses each left point P to "return" to their respective cities that they each previously departed from on the day prior (e.g., the bus that left city M the day prior "returns" to city M). This interpretation leads you to believe that the buses are driving in opposite directions away from each other, which in no way would allow them to "intersect", which the question's answer requires to occur. Unless this is an Official Question, I would recommend that the following example bolded wording needs to be included in the prompt, "...they meet at point P. After returning back to their respective cities the previous day, each bus begins the same route back to point P. One bus is delayed...". Does that make sense? Does anyone else view the language in this question to be misleading? Am I misinterpreting something here?
Regardless, after I chose to go against my belief of what the situation is that the question is portraying, as indicated above, I calculated the problem as if the buses were again each leaving their respective cities and heading towards point P. In this scenario, I used the following calculations:
- each bus requires 2 hours to meet at point P, going at the same speed, thus implying that it takes 4 hours for each bus to travel from M to N or N to M, respectively
- if bus R leaves 36 minutes early, and bus S leaves 24 minutes late, then bus R has a (36+24=60) 1 hour "lead" on bus S
- since bus R was 1 hour in to the drive as compared to bus S, they are (4-1=3) 3 hours apart when bus S begins
- if R and S are traveling at the same speeds, then the buses would meet halfway between the 3 hour mark, which would mean that bus R was driving for (1 hour + 1.5 hours) 2.5 hours and bus S was driving for 1.5 hours (for a total of 4 hours)
- now that you have the meeting points (i.e., original point P = 2 hours, and new meeting point is x+24), you can set up an equation...
- ((2/2.5) = (x/x+24)) --> (2(x+24) = 2.5x) --> (2x+48 = 2.5x) --> 48 = 0.5x --> x = 96
- when plugging x=96 back in to the equation, then 96*2 is the full distance (D)... D=192